We consider a mixed problem with Dirichlet and integral conditions for a second-order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the operator corresponding to the abstract formu...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

In this paper we establish a mean value property for the functions which is satisfied to Laplace–Bessel equation. Our results involve generalized divergence theorem and second Green’s identities relating bulk with boundary of region on differential Bessel operators act. Also design fractional weighted operator, study its boundedness, obtain maximal inequality spherical get boundedness. The conn...

in this paper, we investigate the generalizedhyers--ulam stability of the functional equation

in this paper we obtain  exact solutions of the generalized kuramoto-sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    the methods used  to determine the exact solutions of the underlying equation are the lie group analysis  and the simplest equation method. the solutions obtained are  then plotted.

Here we briefly review our information theoretic approach to revealing community structure in weighted and directed networks [1] and present a new fast stochastic and recursive search algorithm to minimize the map equation — the objective function of our method. We have developed this algorithm to be able to accurately partition the large number of bootstrap networks [2]. The search algorithm c...

The estimation of correlation parameters has received attention for both its own interest and improvement of the estimation efficiency of mean parameters by the generalized estimating equations (GEE) approach. Many of the well-established methods for the estimation of correlation parameters can be constructed under the GEE framework which is, however, sensitive to outliers. In this paper, we co...

The sandwich estimator of variance may be used to create robust Wald-type tests from estimating equations that are sums of K independent or approximately independent terms. For example, for repeated measures data on K individuals, each term relates to a different individual. These tests applied to a parameter may have greater than nominal size if K is small, or more generally if the parameter t...

In this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation. This method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation and ...